We revisit the problem of mitigating information leakage in the widely used but insecure compress-then-encrypt paradigm. While encryption hides message contents, the ciphertext length is directly related to the length of the compressed message, which may, in turn, leak information about the {\em content} of the message itself. Recent work of Blocki et al. (TCC 2025) proposed an (ε,δ)(\varepsilon,\delta)-differentially private approach that adds randomized padding calibrated to the global sensitivit